Nodeless Pairing State in Single-Crystal YBa₂Cu₃O₇

Nodeless Pairing State in Single-Crystal YBa₂Cu₃O₇, D. R. Harshman, W. J. Kossler, X. Wan, A. T. Fiory, A. J. Greer, D. R. Noakes, C. E. Stronach, E. Koster and J. D. Dow

Muon spin rotation (μ⁺SR) measurements were conducted on a single crystal of YBa₂Cu₃O₇ with a superconducting transition temperature of T_C = 91.3 K and a transition width of ΔT_C = 0.5 K in zero applied field. Data were taken at applied magnetic fields along the c-axis of 0.05, 1.0, 3.0, and 6.0 T. We found, by taking into account the expected field-dependent and temperature-activated flux-line disorder, that our results were in fact consistent with a nodeless (s-wave) superconducting order parameter and that they appeared to be inconsistent with order parameters possessing nodes, such as those having d_x²-y² symmetry. This result is consistent with early μ⁺SR measurements on sintered samples in which (we believe) strong pinning eliminated the temperature and field dependence of the vortex lattice disorder. These data (including their observed dependences on magnetic field) are, however, completely consistent with s-wave (or extended s-wave) pairing, provided that field-dependent and temperature-activated vortex depinning is also accounted for. Our results (i) confirm the s-wave superconductivity character originally observed in 1989, and (ii) show that the features of μ⁺SR (and microwave) data claimed by other authors to be evidence for d-wave superconductivity are instead symptomatic of temperature-dependent depinning of vortices, which results in long-ranged distortion of the flux lattice. Indeed, the probability that any published d-wave model gives a better fit than the two-fluid model is less than 4×10^-6.

D. R. Harshman, W. J. Kossler, X. Wan, A. T. Fiory, A. J. Greer, D. R. Noakes, C. E. Stronach, E. Koster and J. D. Dow, Phys. Rev. B 69, 174505 (2004).

The temperature dependence of the magnetic penetration depth in the vortex state of YBa2Cu3O7−δ for H = 0.05, 1.0, 3.0 & 6.0 T, extrapolated to zero-field, with the fitted effects of pinning removed. The data for all four fields are fitted to the two-fluid model, with a London penetration depth of 127.6 +/− 1.5 nm.

Experiment (data from the Comment) and d-wave theory curves for the temperature- and magnetic-field dependence of the inverse-square effective penetration depth of single-crystal YBa2Cu3O6.95. Values of the applied magnetic field H are given in the legend.

Reply to “Comment on ‘Nodeless pairing state in single-crystal YBa₂Cu₃O₇’”
For YBa₂Cu₃O_6.95, both fluxon depinning and a nodeless symmetry of the pairing holes are required to describe the μ⁺SR data. Our work properly identifies and corrects for the effects of fluxon depinning with an activation temperature of about 20 K, and shows that the underlying ground-state symmetry is undoubtedly nodeless in character, consistent with s-wave or extended s-wave pairing. Fluxon depinning has also been independently confirmed by microwave studies indicating activated microscopic vortex pinning at low temperatures. While ignoring the fully established importance of fluxon depinning, Sonier et al. continue to proffer the notion that the μ⁺SR data instead provide evidence of d-wave pairing without fluxon pinning. Even a cursory examination of the published d-wave theories reveals that the predicted low-field linear-in-temperature signature of the d-wave penetration depth
claimed to have been observed in fields H ≥ 0.2 T by Sonier et al. should have been quenched by the magnetic fields applied. The fact that it was not quenched proves that the d-wave conjecture is incorrect: those authors continue to confuse the fluxon depinning evident at ~20 K with a nonexistent d-wave linear term.

D. R. Harshman, W. J. Kossler, X. Wan, A. T. Fiory, A. J. Greer, D. R. Noakes, C. E. Stronach, E. Koster and J. D. Dow, Phys. Rev. B 72, 146502 (2005).